996.
It is well known that F. G. Tricomi (1923) is the originator of the theoryof boundary value problems for mixed type equations by establishing the Thicomi equation: y·u
xx+u
yy=0 which is hyperbolic for y < 0, elliptic for y=0. and parabolic for y= 0 and then applied it in the theory of transonic flows.Then A.V.Bitsadze together with M. A . Lavrent′ev (1950) established the Bitsadze Lavre nt′ev equation: sgn( y ) ·u
xx+u
yy=0 where sgn(y) = 1 for y > 0, = -1 for y<0, 0 for y=0 with the discontinuous coefficient sgn( y ) of u
xx, while in the case of Tricomi equation the corre sponding coefficient y is continuous. In this paper we establish the mixed Bitsadze Lavrent′ev Tricomi equation. Lu=K(y)·u
xx+sgn(x) ·u
yy+r(x,y)·u=f(x,y), where the coefficient K=K(y) of u
xx is increasing continuous and coefficient M=sgn(x) of u
yy discontinuous, r=r(x,y) is once continuously differentiable, f=f(x,y) continuous. Finally we prove the uniqueness of quasi regular solutions and observe that these new results can bbe applied in fluid dynamics.
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